Addition/subtraction of vectors does not require any explicit loop to perform them. Let's take a look at addition of two vectors:

>>> vectorC = vectorA + vectorB
>>> vectorC

The output is shown as follows:

array([8, 8, 8, 8, 8, 8, 8])

Further, we perform subtraction on two vectors:

>>> vectorD = vectorB - vectorA
>>> vectorD

The output is shown as follows:

array([ 6,  4,  2,  0, -2, -4, -6])

Numpy has the built-in function dot to compute the scalar (dot) product between two vectors. We show you its use computing the dot product of vectorA and vectorB from the previous code snippet:

>>> dotProduct1 = numpy.dot(vectorA,vectorB)
>>> dotProduct1

The output is shown as follows:

84

Alternatively, to compute this product we could perform the element-wise product between the components of the vectors and then add the respective results. This is implemented in the following lines of code:

>>> dotProduct2 = (vectorA*vectorB).sum()
>>> dotProduct2

The output is shown as follows:

84

First, two vectors in 3 dimensions are created before applying the built-in function from NumPy to compute the cross product between the vectors:

>>> vectorA = numpy.array([5, 6, 7])
>>> vectorB = numpy.array([7, 6, 5])
>>> crossProduct = numpy.cross(vectorA,vectorB)
>>> crossProduct

The output is shown as follows:

array([-12,  24, -12])

Further, we perform a cross operation of vectorB over vectorA:

>>> crossProduct = numpy.cross(vectorB,vectorA)
>>> crossProduct

The output is shown as follows:

array([ 12, -24,  12])

Notice that the last expression shows the expected result that vectorA cross vectorB is the negative of vectorB cross vectorA.